Tip & Run: The Untold Tragedy of the Great War in Africa by Edward Paice 488pp, Weidenfeld & Nicolson, £25

For Major-General Paul von Lettow-Vorbeck the armistice of November 11 1918, which concluded the first world war, did not come as a surprise. It did not come as anything at all, since von Lettow-Vorbeck, a man who, unlike pretty well any other commander, had succeeded in getting through that bloodbath undefeated, didn't believe the news. If the war was over, he reasoned, then the result would have been favourable to Germany. When told by one Hector Croad, a British district officer in what was then Northern Rhodesia and is now Zambia, that the Kaiser had fled to Holland and Germany was a republic, the "Hindenburg of Africa" dismissed these as clearly outlandish propositions.

But then von Lettow-Vorbeck, the commander of the German army in east Africa, was, even by the standards of the Prussian officer caste, a very special case, a man who went on believing, in an era when eternal verities, empires and Germany's African colonies were to fly out of the window. In 1914 he had been invading British East Africa (today's Kenya) from German East Africa (Tanzania). The Royal Navy dominated the Indian Ocean, and while the numbers of combatants deployed on the continent were minuscule compared to those waging European war, the forces of the British Empire (let alone those of colonial Belgium and Portugal) were vastly superior in numbers to the Kaiser's force in Africa. But von Lettow-Vorbeck's German and African soldiers kept moving, striking out of nowhere.

From March 1916 to August 1918, von Lettow-Vorbeck marched his spectacularly efficient band - plus African porters, who Paice calls "military carriers" - a distance equivalent to that between Paris and St Petersburg. The troops took in German East Africa, Portuguese East Africa (now Mozambique), marched back to German East Africa and then lunged into Northern Rhodesia, eluding the forces of the British Empire - British, Kenyan, Indian, Nigerian, South African et al - en route. But there were other enemies, shared by friend and foe, black, white and brown: typhus, blackwater fever, malaria, cerebro-spinal meningitis, dysentery, smallpox ...

Paice quotes a South African, happy to be heading home in 1917 after fruitlessly chasing another German commander. There were "a handful of Germans hidden in thousands of square miles of bush," he wrote, "[but] the real enemy were the deadly climate, the wild regions, and the swamps and forests and scrub." He could have thrown in, depending on the location, terrifying insects, hippos, crocodiles, lions - with sharks menacing seaplanes hunting the Königsberg. The last German cruiser operating outside Europe was, by 1915, holed up in the Rufiji delta and awaiting destruction at the hands of the Royal Navy, rather than by Humphrey Bogart and Katharine Hepburn's African Queen.

Faced with threats from African nature the Germans proved, as usual, to be splendid improvisers, in medical science as in military arts, with far more doctors on hand than the British - at least until mid-1917. They even made their own quinine, "Lettow Schnapps", from the bark of the cinchona tree.

The personality of von Lettow-Vorbeck is almost as elusive in Tip & Run as the soldier was to his pursuers. Yet it is the major-general who dominates Paice's engrossing, if at times over-detailed narrative, just as that campaign in central and east Africa (west Africa was a comparative walk-over) provides the book's central theme. Von Lettow-Vorbeck's relentlessness, dedication and fanaticism are the stuff of a Conrad novel, but the conclusion of the war, a fortnight after the armistice, hints at the surreal. Paice points out that there were still 34,000 British troops, supported by 71,000 carriers, in the field in east Africa. At Abercorn, in Northern Rhodesia, under rain-filled skies, there were just 155 Germans for von Lettow-Vorbeck to surrender. But then much of this lost world now seems entirely surreal, the Germans encouraging pig-breeding to fend off Islam, while stoking holy war against the British with rumours that the Kaiser had gone over to Mecca.

Tip & Run is a chronicle of so many what-ifs, alternative histories that still shadow that continent now. (What if, for instance, the Germans had been allowed to create a vast colony made up of former Belgian and Portuguese possessions, as the French and British apparently contemplated?) But most of all it is a story of the nightmare shaped by European imperial fantasies and lethally visited on African societies. The warring troops were accompanied by hundreds of thousands of carriers, pressed into servitude. They carried their loads across a terrain where, lurking in the pre-first world war past, there were horrors that would take one more generation to be unleashed on Europe: King Leopold's Congolese holocaust, mass murder in Portuguese slave states and German genocide in South-West Africa. In Paice's account, the British emerge as marginally, just marginally, less awful.

This world was populated with characters out of Rider Haggard and John Buchan: music hall artistes enrolled in the "Legion of Frontiersmen"; adventurers disgracing themselves in the "lowest haunts in Elizabethville"; an intriguing, fleeting reference to two of the few women to get a mention, "Calamity Kate" and "Hellfire Jane", the resident nurses in Zomba, the capital of Nyasaland (now Malawi). There was bush rat pie and ration biscuits smeared with monkey brains as mess fare for the starving and swamped Nigerian Brigade. And then there was Zeppelin L59, sent in 1917 on a doomed German mission to von Lettow-Vorbeck, and ending up 4,340 miles later in Jamboli, Bulgaria, with its crew fevered, frozen and oxygen-starved.

There are no words from the carriers in Paice's book - "the jackal and vulture devour them," wrote a British officer in rain-sodden Nyasaland in November 1917, "each one a hero, though unknown to them". But Paice's numbers do the job. The British official military death toll in east Africa was 11,189; the official figure for carriers who died was 95,000.

Paice estimates that at least 650,000 carriers and civilians died in German Ruanda-Urundi and German East Africa. By 1917-18, with manpower drained from east Africa's land and no rain, famine ensued. Then came the "disease of the wind", the Spanish flu epidemic, and between 1.5 and 2 million died in sub-Saharan Africa.

Meanwhile, von Lettow-Vorbeck ended the war admired as a decent chap by (white) South African and British officers. He sailed back to a different Germany, and got stuck in again. The Spartacists, offering a glimpse of another might-have-been, a revolutionary Germany, had risen up in 1919, and von Lettow-Vorbeck, leading a group of far-right freikorps, crushed them in Hamburg. The following year he took part in the proto-fascist Kapp putsch against the Social Democrats. Paice doesn't speculate, but I suspect von Lettow-Vorbeck was more reactionary conservative than Nazi, though he did keep campaigning for Germany to get its colonies back. And, unlike east Africans in 1918, he just wouldn't die. Von Lettow-Vorbeck was born as the Prussians besieged Paris in 1870, and, outliving JFK, died in 1964, three years after Tanzanian independence, and when the Beatles, rather than the freikorps, preoccupied Hamburg.

· Nigel Fountain's World War II: The People's Story is published by Michael O'Mara/ Readers Digest